Reliability Robust Synthesis Of Planar Path Mechanisms

Mechanisms are taken as a skeleton and a performer of modern mechanical system.Therefore, the quality and the function realizing of mechanical system depend heavily on thekinematic and dynamic performance of mechanisms. With the development of modernscience and technology, mechanical equipment towards high precision, high efficiency, highreliability and long life, this puts forward higher requirement for mechanisms. High kinematicand dynamic performance (such as high motion precision, high kinematic reliability, stabilityand robust, and so on) has become a goal of modern mechanism design. However, how toeffectively deal with the inherent uncertainties of mechanism system is a challenging task forthe high quality mechanism design. At present, introducing the uncertainty design theory andmethod into the real mechanism system design is one of the important topics in the modernmechanism.A path mechanism is used to generate a predetermined (or expectation) path. It’s widelyused in engineering. In this work, kinematic reliability and robust design of path mechanismsare studied. A new model of motion error and the corresponding model of kinematicreliability analysis are presented, and sensitivity of kinematic reliability for mechanisms isdiscussed. Based on the sensitivity of the kinematic reliability, the robust design method ofpath mechanisms is proposed. The main contents are as follows.1. To analyze the comprehensive kinematic reliability of path mechanism at a specificinstant time, a new motion error model of path generation mechanisms is proposed. Based onkinematic analysis, the probabilistic model of motion error of path generation mechanisms iscreated, and the calculate formula of kinematic reliability of path generation mechanisms isderived.2. Considering the nonlinearity of kinematic reliability analysis model, the first orderreliability method (FORM) is applied to solve the model. To improve accuracy of the result, ahybrid optimization algorithm, which combined with the genetic algorithm (GA) andsequential quadratic programming (SQP), is proposed to solve the Most Probable Point(MPP). Numerical examples indicate the accuracy of the algorithm is satisfied.3. Based on the kinematic reliability analysis model, the reliability sensitivity formulasof path generation mechanisms is derived. A planar four-bar path generation mechanism istaken as a numerical example to illustrate this kinematic reliability sensitivity model.4. Based on reliability sensitivity analysis, the robust synthesis model of a planarfour-bar path generation mechanism is presented. In this synthesis model, minimum reliabilitysensitivities of dimension variables are taken as objective functions, and kinematic reliability and dynamic performance are taken as design constraints. A planar four-bar path generationmechanism is taken as a numerical example to illustrate this robust synthesis method.